It is known to provide a pipe connection between one end of a pipe made of a plastic material that has memory properties and a connecting piece. The memory properties mean that plastic pipes with a memory capacity automatically tend to return essentially to their original shape and form after having been expanded. For example plastic pipes that are manufactured from cross-linked polyethylene possess an active memory capacity at temperatures as low as room temperature. Pipes of this nature are joined together by widening one end of the pipe and inserting into the widened pipe end a flanged connector which forms a part of the pipe-connecting piece, normally made of metal, and which is retained in said pipe end until the pipe has shrunk to an extent at which it is able to firmly hold the connecting piece. A clamping ring made of elastic material, which may be the same plastic material as that from which the pipe is made, is expanded and shrunk over the pipe end in order to further enhance the holding and sealing pressure at the pipe connection region. The clamping ring is expanded at the same time as the pipe end is expanded, with the clamping ring in position around said pipe end. Such a solution has been disclosed for example in EP 0 530 387. In EP 0 530 387 the clamping ring has been made from an extruded pipe by cutting the pipe into a short enough part to form a clamping ring. In WO 2009/004407 the clamping ring has also been made by cutting an extruded pipe to form a pipe part and bending the end of the pipe part such that a clamping ring having a stop edge is formed. In EP 1 741 968 the clamping ring is made by injection molding.